Normal Modes and Localization in Nonlinear Systems

The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is c

Based on a successful text, this second edition presents different concepts from dynamical systems theory and nonlinear dynamics. The introductory text systematically introduces models and techniques

This work addresses time-delay in complex nonlinear systems and, in particular, its applications in complex networks; its role in control theory and nonlinear optics are also investigated. Delays aris

There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact

The physics and mathematics of nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developments of late twentieth-century science. It turns out that chaotic behaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavour. In this book, two dozen scientists and mathematicians who were deeply involved in the 'nonlinear revolution' cover most of the basic aspects of the field. The book is divided into five parts: dynamical systems, bifurcation theory and chaos; spatially extended systems; dynamical chaos, quantum physics and the foundations of statistical mechanics; evolutionary and cognitive systems; and complex systems as an interface between the sciences.

Dynamical Systems: Discontinuity, Stochasticity and Time-Delay provides an overview of the most recent developments in nonlinear dynamics, vibration and control. This book focuss on the most recent a

Nuclear Superfluidity is an advanced text devoted exclusively to pair correlations in nuclei. It begins by exploring pair correlations in a variety of systems including superconductivity in metals at low temperatures and superfluidity in liquid 3He and in neutron stars. The book goes on to introduce basic theoretical methods, symmetry breaking and symmetry restoration in finite many-body systems. The last four chapters are devoted to introducing results on the role of induced interactions in the structure of both normal and exotic nuclei. The most important of these is the renormalization of the pairing interaction due to the coupling of pairs of nucleons to low energy nuclear collective excitations. This book will be essential reading for researchers and students in both experimental and theoretical nuclear physics, and related research fields such as metal clusters, fullerenes and quantum dots.

In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamic

Advances in public management sciences have long indicated the empirical finding that the normal state of public management systems is complex and that its dynamics are non-linear. Complex systems ar

Nonlinear dynamics has become an important field of research in recent years in many areas of the natural sciences. In particular, it has potential applications in biology and medicine; nonlinear dat

Written for maximum flexibility, this best-selling junior level mechanics text is easily adaptable to any length--one- or two-semester--or focus of course.LAGRANGIAN and HAMILTONIAN DYNAMICS are introduced early in the text.This text has an entire chapter on NONLINEAR METHODS.NUMERICAL METHODS PROBLEMS are included for students to solve using a computer.

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysi

The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.

This 1992 book surveys the field of ultrafast fiber switching devices and systems that have potential processing speeds in excess of 50 gigabits-per-second. The treatment covers basic physical principles, device physics and systems applications. The purpose of the book is to provide a complete tour of the key research issues and approaches in ultrafast switching. Topics covered include routing and logic devices, solitons in optical fibers, and the application of ultrafast gates to telecommunications transmission systems, local area networks and optical computing. The author is a member of the Technical Staff in basic research at AT&T Bell Laboratories, Holmdel, and is excellently positioned to provide this state-of-the-art survey in this exciting and advancing field. The book will be of great value to all researchers and graduate students working in the areas of high-speed electronics, optical data processing, nonlinear guided-wave optics, and photonic switching.

Developments in sensor and processor sophistication have created a need for effective estimation and control algorithms for hybrid, nonlinear systems. This book presents an effective, flexible family of estimation algorithms that can be used in estimating or controlling a variety of nonlinear plants. Several applications are studied, including tracking a manoeuvring aircraft, automatic target recognition, and the decoding of signals transmitted across a wireless communications link. The authors begin by setting out the necessary theoretical background and then develop a practical, finite-dimensional approximation to an optimal estimator. Throughout the book, they illustrate theoretical results by simulation of control and estimation in real-world hybrid systems, drawn from a variety of engineering fields. The book will be of great interest to graduate students and researchers in electrical and computer engineering. It will also be a useful reference for practising engineers involved in

Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semicon

Nuclear Superfluidity is an advanced text devoted exclusively to pair correlations in nuclei. It begins by exploring pair correlations in a variety of systems including superconductivity in metals at low temperatures and superfluidity in liquid 3He and in neutron stars. The book goes on to introduce basic theoretical methods, symmetry breaking and symmetry restoration in finite many-body systems. The last four chapters are devoted to introducing results on the role of induced interactions in the structure of both normal and exotic nuclei. The most important of these is the renormalization of the pairing interaction due to the coupling of pairs of nucleons to low energy nuclear collective excitations. This book will be essential reading for researchers and students in both experimental and theoretical nuclear physics, and related research fields such as metal clusters, fullerenes and quantum dots.

Pang (U. of Electronic Science and Technology of China) and Feng (National U. of Singapore) explain the properties of microscopic particles in nonlinear systems and the principles of the nonlinear qua

This book presents a rare mix of the latest mathematical theory and procedures in the area of nonlinear difference equations and discrete dynamical systems, together with applications of this theory t

Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semicon

When a mechanical system consists of two or more coupled vibrating components, the vibration of one of the component subsystems may destabilize the motion of the other components. This destabilization effect is called autoparametric resonance. It is a concept that has important engineering applications. For example, vibrations in a pipeline induced by high-speed gas flows must be considered in the design and operation of the pipeline. This book is the first completely devoted to the subject of autoparametric resonance in an engineering context. Using the tools of nonlinear analysis, the authors show how to carry out the first crucial step, that is, how to determine the regions of parameter space where the semi-trivial solution is unstable. They describe what happens in these regions and then discuss non-trivial solutions and their stability. The study of autoparametric systems is a lively area of current research in engineering and applied mathematics, and this book will appeal to gra

"Requirements engineering is a discipline used primarily for large and complex applications. It is more formal than normal methods of gathering requirements, and this formality is needed for many larg

Developments in sensor and processor sophistication have created a need for effective estimation and control algorithms for hybrid, nonlinear systems. This book presents an effective, flexible family of estimation algorithms that can be used in estimating or controlling a variety of nonlinear plants. Several applications are studied, including tracking a manoeuvring aircraft, automatic target recognition, and the decoding of signals transmitted across a wireless communications link. The authors begin by setting out the necessary theoretical background and then develop a practical, finite-dimensional approximation to an optimal estimator. Throughout the book, they illustrate theoretical results by simulation of control and estimation in real-world hybrid systems, drawn from a variety of engineering fields. The book will be of great interest to graduate students and researchers in electrical and computer engineering. It will also be a useful reference for practising engineers involved in

Self-organized criticality (SOC) is based upon the idea that complex behavior can develop spontaneously in certain multi-body systems whose dynamics vary abruptly. This book is a clear and concise introduction to the field of self-organized criticality, and contains an overview of the main research results. The author begins with an examination of what is meant by SOC, and the systems in which it can occur. He then presents and analyzes computer models to describe a number of systems, and he explains the different mathematical formalisms developed to understand SOC. The final chapter assesses the impact of this field of study, and highlights some key areas of new research. The author assumes no previous knowledge of the field, and the book contains several exercises. It will be ideal as a textbook for graduate students taking physics, engineering, or mathematical biology courses in nonlinear science or complexity.

In this introductory textbook, a revised and extended version of well-known lectures by L. Hormander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from

The physics and mathematics of nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developments of late twentieth-century science. It turns out that chaotic behaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavour. In this book, two dozen scientists and mathematicians who were deeply involved in the 'nonlinear revolution' cover most of the basic aspects of the field. The book is divided into five parts: dynamical systems, bifurcation theory and chaos; spatially extended systems; dynamical chaos, quantum physics and the foundations of statistical mechanics; evolutionary and cognitive systems; and complex systems as an interface between the sciences.

This book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of Lie algebras and differential geometry with an emphasis on further applications to integrable nonlinear systems. Chapter 3 contains a derivation of Toda type systems and their general solutions based on Lie algebra and differential geometry methods. The last chapter examines explicit solutions of the corresponding equations. The book is written in an accessible 'lecture note' style with many examples and exercises to illustrate key points and to reinforce understanding.

The second edition of this textbook, popular amongst students and faculty alike, investigates the various causes of thermodynamic instability in metallic microstructures. Materials theoretically well designed for a particular application may prove inefficient or even useless unless stable under normal working conditions. The authors examine current experimental and theoretical understanding of the kinetics behind structural change in metals. The entire text has been updated in this new edition, and a completely new chapter on highly metastable alloys has been added. The degree to which kinetic stability of the material outweighs its thermodynamic instability is very important, and dictates the useful working life of the material. If the structure is initially produced to an optimum, such changes will degrade the properties of the material. This comprehensive and well-illustrated text, accompanied by ample references, will allow final year undergraduates, graduate students and research

By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.

Almost all the many past studies on chaos have been concerned with classical systems. This book, however, is one of the first to deal with quantum chaos, the natural progression from such classical systems. In this book the author deals with three major issues in quantum chaos. First, quantum mechanics is applied to both bounded and open systems exhibiting classical chaos. Potential problems involving quantum chaos are revealed in diverse areas of solid-state science, and standard concepts such as diamagnetism, antiferromagnetism, spin waves, electrical conductance and so on are shown in a fresh light through quantum chaos. Second, adiabatic-ansatz eigenvalue problems are shown to yield a new paradigm of non-linear dynamics, closing the gap between the greatly different theories of solitons and random matrices. Finally, the author provides a clue to how quantum mechanics may be improved so as to accommodate temporal chaos. First published in 1993, this book will be of value to researc

This 1992 book surveys the field of ultrafast fiber switching devices and systems that have potential processing speeds in excess of 50 gigabits-per-second. The treatment covers basic physical principles, device physics and systems applications. The purpose of the book is to provide a complete tour of the key research issues and approaches in ultrafast switching. Topics covered include routing and logic devices, solitons in optical fibers, and the application of ultrafast gates to telecommunications transmission systems, local area networks and optical computing. The author is a member of the Technical Staff in basic research at AT&T Bell Laboratories, Holmdel, and is excellently positioned to provide this state-of-the-art survey in this exciting and advancing field. The book will be of great value to all researchers and graduate students working in the areas of high-speed electronics, optical data processing, nonlinear guided-wave optics, and photonic switching.

'Et mai ‧...‧ si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost

Thirty-five articles detailing the applications of nonlinear analysis to the theory of nuclear reactors, and the role of noise in detecting abnormalities assocated with nonlinear processes. Major conc

The science of rheology and its applications have grown steadily. Although polymers dominated in the past, the applications to foods have become increasingly important over the last four decades. The complexity of food rheology has not only generated increased interest among academics, but it has also led to an increased recognition of its importance in the food industry. Emphasizing physics rather than mathematics, Polymer and Food Rheology: Volume 1, Applications to Single-Phase Systems focuses on rheological characteristics and properties of single substances and homogeneous mixtures. It introduces fundamental principles, types of flows, types of instruments, their theory, capabilities, limitations, and sources of error. Both sophisticated rheometers and simple devices and their uses are considered.- Discusses the types of material functions (properties) obtained from the different types of measurements and techniques: shear viscosity, normal stress differences, dynamic mechanical p

Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential

In modern-day Hong Kong, major constitutional controversies have caused people to demonstrate on the streets, immigrate to other countries, occupy major thoroughfares, and even engage in violence. These controversies have such great resonance because they put pressure on a cultural identity made possible by, and inseparable from, the 'One Country, Two Systems' framework. Hong Kong is also a city synonymous with film, ranging from commercial gangster movies to the art cinema of Wong Kar-wai. This book argues that while the importance of constitutional controversies for the process of self-formation may not be readily discernible in court judgments and legislative enactments, it is registered in the diverse modes of expression found in Hong Kong cinema. It contends that film gives form to the ways in which Hong Kong identity is articulated, placed under stress, bolstered, and transformed in light of disputes about the nature and meaning of the city's constitutional documents.

In modern-day Hong Kong, major constitutional controversies have caused people to demonstrate on the streets, immigrate to other countries, occupy major thoroughfares, and even engage in violence. These controversies have such great resonance because they put pressure on a cultural identity made possible by, and inseparable from, the 'One Country, Two Systems' framework. Hong Kong is also a city synonymous with film, ranging from commercial gangster movies to the art cinema of Wong Kar-wai. This book argues that while the importance of constitutional controversies for the process of self-formation may not be readily discernible in court judgments and legislative enactments, it is registered in the diverse modes of expression found in Hong Kong cinema. It contends that film gives form to the ways in which Hong Kong identity is articulated, placed under stress, bolstered, and transformed in light of disputes about the nature and meaning of the city's constitutional documents.

A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will